Fuzzy importance measures for ranking key interdependent sectors under uncertainty

In the field of reliability engineering, several approaches have been developed to identify those components that are important to the operation of the larger interconnected system. We extend the concept of component importance measures to the study of industry criticality in a larger system of economically interdependent industry sectors that are perturbed when underlying infrastructures are disrupted. We provide measures of (i) those industries that are most vulnerable to disruptions and (ii) those industries that are most influential to cause interdependent disruptions. However, difficulties arise in the identification of critical industries when uncertainties exist in describing the relationships among sectors. This work adopts fuzzy measures to develop criticality indices, and we offer an approach to rank industries according to these fuzzy indices. Much like decision makers with the knowledge of the most critical components in a physical system, the identification of these critical industries provides decision makers with priorities for resources. We illustrate our approach with an interdependency model driven by US Bureau of Economic Analysis data to describe industry interconnectedness.